Game-Theoretic Applications of Pentagonal Fuzzy Numbers Through New Representation and Defuzzification Schemes

Abstract

This research paper presents novel insights into the representation, ranking, and defuzzification of pentagonal fuzzy numbers. The fundamental foundation of this study lies in the development of a robust pentagonal fuzzy number, which is explored through diverse representations that harness the principles of continuity within the membership function. To facilitate practical implementation, a variety of defuzzification methods are meticulously applied, resulting in the transformation of fuzzy data into crisp. The significance of pentagonal fuzzy numbers is further illuminated through their application in the context of game theory, specifically within the domain of matrix games. This strategic analysis explains the pragmatic relevance of pentagonal fuzzy numbers in deciphering complex real-world scenarios and optimizing decision-making processes. Theoretical constructs are bolstered by numerical examples, empirically showcasing the practical applicability of the developed theory.